ECE 4371, Fall, 2015

Introduction to Telecommunication Engineering/Telecommunication Laboratory

Zhu Han

Department of Electrical and Computer Engineering

Class 17

Oct. 20th, 2015

                                                           

                                                           

OutlineOutline Project 2, Due 12/1

Exam 2, 11/24

Term project

ARQ

FEC Basics

                                                           

Project 2 Project 2 Due 12/1/14 Take a selfie Show time signal, eye diagram, and constellation for no noise, SNR=0,

SNR=5dB and SNR=10dB. (1 point) Calculate BER for SNR=0. SNR=2.5dB and SNR=5dB, compared with

theoretic result. Change symb to sufficiently large. (2 point) For QPSK and 16QAM, redo the above step (2 point) Transmit images (3 point)

– Test small image first– Alignment for both sampling and data– Calculate PSNR for SNR=0dB, SNR=2.5dB, and SNR=5dB. – Print images

Timing: sampling at the wrong time. 2 point– 1/16, 2/16, … for BER vs. SNR, PSNR vs. SNR

                                                           

ISIISI

0 2 4 6 8 10 12 14 16-1.5

-1

-0.5

0

0.5

1

1.5

2

                                                           

Scatter PlotScatter Plot

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Qua

drat

ure

In-Phase

Scatter plot

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

Qua

drat

ure

In-Phase

Scatter plot

                                                           

Eye DiagramEye Diagram

-0.5 0 0.5-1.5

-1

-0.5

0

0.5

1

1.5

Time

Am

plitu

de

Eye Diagram

-0.5 0 0.5-2

-1

0

1

2

Time

Am

plitu

de

Eye Diagram for In-Phase Signal

-0.5 0 0.5-2

-1

0

1

2

Time

Am

plitu

de

Eye Diagram for Quadrature Signal

                                                           

BER and PSNR vs. SNRBER and PSNR vs. SNR Error Floor for sampling errors

0 1 2 3 4 510

-3

10-2

10-1

100

EbNo (dB)

SE

R a

nd B

ER

Performance of Baseband QPSK

Theoretical SER

Theoretical BERSimulated SER

Simulated BER

SNR

PSNR

                                                           

ImageImage Original, 5 dB, 2.5 dB, 0 dB, and

                                                           

Technical WritingTechnical Writing Structure, Logic (between sentences and paragraphs), and Strictness (no holes). Know who is your audiences Structure

– Title and keyword: concise and hit the point, for google users– Abstract: 200 words, for directors who have 20 seconds

Why it is a good topic What is the idea and contribution What are the results

– Introduction: 1 pages, for managers who have 5 minutes Why it is a good topic What are in the literature, or what are the competitors What is the idea and contribution What are the results (Organization)

– System model– Problem formulation, proposed scheme, and analysis– Results– Conclusions– Citations

For peer

                                                           

Term Project, Choice OneTerm Project, Choice One Due at last regular class so that I can talk about it during

additional class.

Goal: If you have interview on company for wireless project xxx, what you should know

Source– The company listed on the web or some company you know.

– Select the cool project interesting you. Send me an email by 11/10

Structure– Abstract: 100 words for the company, the project and why interests

– Introduction: 1 pages for the company: history, competitors, project lines, future, stocks, etc.

– Main body of 3 pages for a specific product: 2 pages for the thing you have studied from this class, 1 page for something new.

                                                           

Term Project, Choice twoTerm Project, Choice two What is the state of art of xxx

– Bluetooth, UWB, WLAN, WMAN, 3G, Ad hoc/Sensor Networks

Cognitive Radio, Fiber communication, Cable communication,

Power line communication, Satellite communication, etc.

Source– IEEE communication magazine to get some tutorial papers– Important citations can be found by IEEE Xplore– Citeseer to test if the paper is well cited and recognized– Select a topic by 11/10.

Writing– Goal: suppose you were me and want to give a lecture on the state of art

of xxx.– 200 words abstract, 1 page introduction and 3 pages details, excluding

the figures.– Citations are needed if you “copy” some ideas.

                                                           

Automatic Repeat-reQuest (ARQ)Automatic Repeat-reQuest (ARQ)

Alice and Bob on their cell phones– Both Alice and Bob are talking

What if Alice couldn’t understand Bob?– Bob asks Alice to repeat what she said

What if Bob hasn’t heard Alice for a while?– Is Alice just being quiet?

– Or, have Bob and Alice lost reception?

– How long should Bob just keep on talking?

– Maybe Alice should periodically say “uh huh”

– … or Bob should ask “Can you hear me now?”

                                                           

ARQARQ Acknowledgments from receiver

– Positive: “okay” or “ACK”

– Negative: “please repeat that” or “NACK”

Timeout by the sender (“stop and wait”)– Don’t wait indefinitely without receiving some response

– … whether a positive or a negative acknowledgment

Retransmission by the sender– After receiving a “NACK” from the receiver

– After receiving no feedback from the receiver

                                                           

Error Correcting CodesError Correcting Codes

Adding redundancy to the original message To detect and correct errors Crucial when it’s impossible to resend the message

(interplanetary communications, storage..) and when the channel is very noisy (wireless communication)Information

Source

Message

Transmitter

Noise Source

Destination

Message

Reciever

ReceivedSignal

Signal

Message = [1 1 1 1]

Noise = [0 0 1 0]

Message = [1 1 0 1]

                                                           

Types of Error Correcting CodesTypes of Error Correcting Codes Repetition Code

Linear Block Code, e.g. Hamming

Cyclic Code, e.g. CRC

BCH and RS Code

Convolutional Code– Tradition, Viterbi Decoding

– Turbo Code

– LDPC Code

Coded Modulation– TCM

– BICM

                                                           

Repetition CodeRepetition Code

Simple Example: reduce the capacity by 3Simple Example: reduce the capacity by 3

Recovered state

                                                           

Parity CheckParity Check Add one bit so that xor of all bit is zero

– Send, correction, miss

– Add vertically or horizontally

Applications: ASCII, Serial port transmission

                                                           

ISDN NumberISDN Number ISBN 10

– a modulus 11 with weights 10 to 2, using X instead of 10 where ten would occur as a check digit

– ISBN 0-306-40615-2

ISBN 13– Calculating an ISBN 13 check digit requires

that each of the first twelve digits of the 13-digit ISBN be multiplied alternately by 1 or 3. Next, take the sum modulo 10 of these products. This result is subtracted from 10.

– ISBN 978-0-306-40615-7.

                                                           

Hammings SolutionHammings Solution

A type of Linear Block Code

Encoding: H(7,4)

Multiple ChecksumsMessage=[a b c d]

r= (a+b+d) mod 2s= (a+b+c) mod 2t= (b+c+d) mod 2

Code=[r s a t b c d]

Coding rate: 4/7– Smaller, more redundancy, the better protection.

– Difference between detection and correction

Message=[1 0 1 0] r=(1+0+0) mod 2 =1

s=(1+0+1) mod 2 =0

t=(0+1+0) mod 2 =1

Code=[ 1 0 1 1 0 1 0 ]

                                                           

Error Detection AbilityError Detection Ability

100,000 iterationsAdd Errors to (7,4) dataNo repeat randomsMeasure Error Detection

Error Detection•One Error: 100%•Two Errors: 100% •Three Errors: 83.43%•Four Errors: 79.76%

Stochastic Simulation:

Results:

Fig 1: Error Detection

50%

60%

70%

80%

90%

100%

1 2 3 4Errors Introduced

Per

cen

t E

rro

rs D

etec

ted

(%

)

                                                           

How it works: 3 dotsHow it works: 3 dots

Only 3 possible words

Distance Increment = 1

One Excluded State (red)

It is really a checksum.

Single Error Detection

No error correction

A B C

A B C

A C

Two valid code words (blue)

This is a graphic representation of the “Hamming Distance”

                                                           

Hamming DistanceHamming Distance

Definition: – The number of elements that need to be changed (corrupted) to turn one

codeword into another.

The hamming distance from:– [0101] to [0110] is 2 bits

– [1011101] to [1001001] is 2 bits

– “butter” to “ladder” is 4 characters

– “roses” to “toned” is 3 characters

                                                           

Another DotAnother Dot

The code space is now 4.

The hamming distance is still 1.

Allows:

Error DETECTION for Hamming Distance = 1.

Error CORRECTION for Hamming Distance =1

For Hamming distances greater than 1 an error gives a false correction.

                                                           

Even More DotsEven More Dots

Allows:Error DETECTION for Hamming Distance = 2.

Error CORRECTION for Hamming Distance =1.

• For Hamming distances greater than 2 an error gives a false correction.

• For Hamming distance of 2 there is an error detected, but it can not be corrected.

                                                           

Multi-dimensional CodesMulti-dimensional Codes

Code Space:

• 2-dimensional

• 5 element states

Circle packing makes more efficient use of the code-space

                                                           

Cannon BallsCannon Balls

http://wikisource.org/wiki/Cannonball_stacking

http://mathworld.wolfram.com/SpherePacking.html

Efficient Circle packing is the same as efficient 2-d code spacing

Efficient Sphere packing is the same as efficient 3-d code spacing

Efficient n-dimensional sphere packing is the same as n-code spacing

                                                           

ExampleExample Visualization of eight code words in a 6-typle space